Recent content by Lie

Thanks! I showed that Y is locally compact space and therefore is compactly generated space. Grateful.

Yes, I had forgotten: F to be continuous and Y (X and) to be Hausdorff. :) Compactly generated = union of open compact ? Thanks... :)

Hello! F: X --> Y injection. It is true that if F is proper (the inverse image of any compact set is compact) then F: X --> F(X) is a homeomorphism? Thanks... :)

Excuse me! I was very busy lately and I could not move from here. Not found any error! Thank very much. :)

Indeed! :) Tip of Hewitt & Ross! ;)

OK! I don't really need Hausdorff. The natural mapping g of G onto G/H is a closed mapping, continuous, surjective and every g^{-1}(xH) is closed. Why it's proper? This result is interesting, but I would try to use my argument above. Thankful! :)

Can I do that G/H is not a group? Remember that H is only one subgroup. It is not normal!

No! I don't understand!

Hello! Could anyone help me to resolve the impasse below? Th: Let G be a topological group and H subgroup of G. If H and G/H (quotient space of G by H) are compact, then G itself is compact. Proof: Since H is compact, the the natural mapping g of G onto G/H is a closed mapping...

I did it! ;)

Hello! Does anyone have any idea how to show that every dense G_\delta-subspace of a Baire space is a Baire space? Grateful.

Jamma, same remark:

micromass, Note that condition 3 implies that the algebra can not have unity. Therefore \mathbb{Z}_2[X]/(X^3) is not an example.

Anyone know of an example of an algebra over the field \mathbb{Z}_2 with the following properties? 1. commutative; 2. associative; 3. x^3 = 0 , for all x; and 4. Exists x and y such that x^2y \neq 0 . Grateful!